Black hole interiors and temporal completion: SMM/DTT and ΛCDM cosmology

01The question behind this comparison

Black-hole interiors test whether a theory can connect local physics, causal horizons and global information consistently. Classical general relativity describes a horizon and, in simple solutions, an interior singularity. Quantum field theory on that background predicts Hawking radiation in an appropriate state. A complete microscopic account would explain the quantum degrees of freedom and their evolution beyond the regime of the semiclassical approximation.

DTT’s retained-source picture offers a way to distinguish inaccessible information from destroyed information. An exterior completed archive may omit relations still present in the full source. That distinction is useful, but it does not itself solve the information problem: the theory must show how the final accessible state is related to the initial state and how its entropy evolves. A hidden archive that never influences observable radiation is not automatically a unitary evaporation mechanism. ^{[3] [4] [5]}

02The SMM/DTT starting point

The Single Monad Model begins with one nonspatial generative source. The Duality of Time Theory distinguishes the source’s inner production from the outer order in which completed records become accessible. Its six inner levels are nested functional roles of one process: a higher role organizes lower-level work. The seventh is the completion or observation interface. They are neither six independent clocks nor six additional time coordinates.

This distinction supplies a useful research question: which features of an observed world can follow from the way a source produces, retains and releases information? A concrete answer needs a state space, an autonomous update, retained memory and a rule connecting completion to an accessible measurement. In the constructions discussed here, those mathematical ingredients are stated explicitly. A successful finite example establishes what its specified mechanism can do; further arguments connect it to physical particles, spacetime or universal laws. ^[1]

03How the comparator works

ΛCDM is a quantitative cosmological model combining a cosmological constant, cold dark matter, ordinary matter, radiation and specified primordial perturbations. Its parameters are inferred jointly from observations through dynamical evolution and transfer functions. A successful fit to cosmic expansion and structure does not by itself identify the microscopic nature of dark matter or explain the small observed vacuum energy. The Planck 2018 analysis is used here as a named, dated benchmark for the model’s predictive organization.

DTT can be an underlying proposal for why such an effective cosmology arises, or it can become an alternative cosmology if it changes the equations or initial conditions. Those are different tasks. To make the second claim, a source model needs distances, redshifts, physical clocks and perturbation observables calculated from one consistent solution. Matching a single constant or a qualitative picture of continual creation cannot replace the simultaneous constraints on expansion, lensing and structure. Conversely, reproducing ΛCDM as a limit could be a useful result even before a distinct observational correction is established. ^[2]

04The decisive comparison

ΛCDM supplies the large-scale cosmological environment in which astrophysical black holes form and evolve; it is not a microscopic theory of their interiors. DTT’s temporal-completion proposal addresses a different explanatory layer. It can be compared with the cosmological model through formation history, expansion and observable exterior effects, while the information mechanism needs separate quantum dynamics.

The Schwarzschild benchmark deliberately isolates an idealized object from that environment. Its temperature and entropy scalings must be recovered before a proposed source modification is inserted into cosmological populations. Accretion, spin and ambient radiation can dominate an actual black hole’s evolution, so a hidden completion effect cannot be inferred from a simplified evaporation story alone. DTT’s potential unification would connect the same source parameters to vacuum cosmology and black-hole records. That would be a valuable cross-scale restriction, provided the parameters are not independently retuned in each setting. The comparison therefore distinguishes compatibility with a successful background cosmology from a claim to explain black-hole microphysics. A universal source ontology links the questions conceptually; a common dynamical solution must link them physically. ^{[2] [3] [4] [5]}

05Worked benchmark

For a nonrotating, uncharged black hole, the Schwarzschild radius is rs=2GM/c² and the Hawking temperature is TH=ℏc³/(8πGMkB). Doubling the mass doubles the radius and halves the temperature. Its Bekenstein–Hawking entropy scales as M², so doubling the mass multiplies the entropy by four. These different scalings constrain any proposed source capacity and release law simultaneously.

For an illustrative solar-mass black hole, rs is about 2.95 kilometres and TH about 6.2×10⁻⁸ kelvin. These are semiclassical predictions for the stated idealized system, not direct laboratory measurements of its radiation. A DTT model that uses completion events as radiation emissions must recover the thermal low-order spectrum in this regime while also specifying the correlations needed for unitary information recovery. A curve that reproduces only the temperature does not decide whether the radiation’s fine-grained entropy ultimately decreases. ^{[3] [4] [5]}

06What follows for the source programme

The strongest source-based contribution would be a finite model with a controlled exterior limit, an explicit internal memory and a demonstrably unitary transfer of information into radiation. Island calculations provide a separate benchmark for entropy in certain controlled gravitational models. Reproducing their qualitative Page-curve shape is insufficient by itself; the microphysical map and its domain of validity remain central to the explanatory claim. ^{[3] [4] [5]}

THE SAME QUESTION, DIFFERENT STARTING POINTS

The comparison at a glance

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